Question: Simplify the following expression: $r = \dfrac{-9q^2 + 99q - 270}{q - 5} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-9$ , so we can rewrite the expression: $ r =\dfrac{-9(q^2 - 11q + 30)}{q - 5} $ Then we factor the remaining polynomial: $q^2 {-11}q + {30} $ ${-5} {-6} = {-11}$ ${-5} \times {-6} = {30}$ $ (q {-5}) (q {-6}) $ This gives us a factored expression: $\dfrac{-9(q {-5}) (q {-6})}{q - 5}$ We can divide the numerator and denominator by $(q + 5)$ on condition that $q \neq 5$ Therefore $r = -9(q - 6); q \neq 5$